DYKSTRAS ALGORITHM FOR A CONSTRAINED LEAST-SQUARES MATRIX PROBLEM

We apply Dykstra's alternating projection algorithm to the constrained least-squares matrix problem that arises naturally in statistics and mathematical economics. In particular, we are concerned with the probl em of finding the closest symmetric positive definite bounded and patt erned matrix, in the Frobenius norm, to a given matrix. In this work, we state the problem as the minimization of a convex function over the intersection of a finite collection of closed and convex sets in the vector space of square matrices. We present iterative schemes that exp loit the geometry of the problem, and for which we establish convergen ce to the unique solution. Finally, we present preliminary numerical r esults to illustrate the performance of the proposed iterative methods .